Finite Element Methods for Sobolev Equations

Finite Element Methods for Sobolev Equations

Year:    2002

Author:    Liu Tang, Shu-Hua Zhang, J. R. Cannon, Yan-Ping Lin, Ming Rao

Journal of Computational Mathematics, Vol. 20 (2002), Iss. 6 : pp. 627–642

Abstract

A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method are derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2002-JCM-8948

Journal of Computational Mathematics, Vol. 20 (2002), Iss. 6 : pp. 627–642

Published online:    2002-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Error estimates finite element Sobolev equation numerical integration.

Author Details

Liu Tang

Shu-Hua Zhang

J. R. Cannon

Yan-Ping Lin

Ming Rao